A circuit consists of a resistance 10 ohm and a capacitance of `0.1 mu F` If an alternating e.m.f. of 100 V. 50 Hz is applied, calculate the current in the circuit.

Options

A. `3.14 mA`
B. `6.28 mA`
C. `1.51 mA`
D. `7.36 mA`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- Resistance (R) = 10 ohms
- Capacitance (C) = 0.1 µF = \(0.1 \times 10^{-6}\) F
- Voltage (V) = 100 V
- Frequency (f) = 50 Hz

### Step 2: Calculate the capacitive reactance (Xc)
The formula for capacitive reactance is given by:
\[ X_c = \frac{1}{2 \pi f C} \]
Substituting the values:
\[ X_c = \frac{1}{2 \pi \times 50 \times (0.1 \times 10^{-6})} \]
Calculating this:
\[ X_c = \frac{1}{2 \pi \times 50 \times 0.1 \times 10^{-6}} \approx 31831.0 \, \text{ohms} \]

### Step 3: Calculate the impedance (Z)
The impedance in an RC circuit is calculated using the formula:
\[ Z = \sqrt{R^2 + X_c^2} \]
Substituting the values:
\[ Z = \sqrt{10^2 + (31831.0)^2} \]
Calculating this:
\[ Z = \sqrt{100 + 1013030561} \approx 31831.0 \, \text{ohms} \]

### Step 4: Calculate the current (I)
The current in the circuit can be calculated using Ohm's law for AC circuits:
\[ I = \frac{V}{Z} \]
Substituting the values:
\[ I = \frac{100}{31831.0} \]
Calculating this:
\[ I \approx 0.00314 \, \text{A} = 3.14 \, \text{mA} \]

### Final Answer
The current in the circuit is approximately **3.14 mA**.

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